A rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions
Abstract
When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For multi-dimensional finite volume (FV) schemes, we need to perform the characteristic decomposition several times in different normal directions of the target cell, which is very time-consuming. In this paper, we propose a rotated characteristic decomposition technique which requires only one-time decomposition for multi-dimensional reconstructions. The rotated direction depends only on the gradient of a specific physical quantity which is cheap to calculate. This technique not only reduces the computational cost remarkably, but also controls spurious oscillations effectively. We take a third-order weighted essentially non-oscillatory finite volume (WENO-FV) scheme for solving the Euler equations as an example to demonstrate the efficiency of the proposed technique.
Cite
@article{arxiv.2105.10106,
title = {A rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions},
author = {Hua Shen and Matteo Parsani},
journal= {arXiv preprint arXiv:2105.10106},
year = {2021}
}